Add wine, lime juice, and shallots to skillet; boil over high heat 2 to 3 minutes, until liquid is reduced to about 1 1/2 tablespoons. Stir in cream. Once mixture bubbles, reduce heat to low. Swirl in butter one piece at a time, adding each piece before the previous one has completely melted. Lift pan from heat a few times so sauce won't separate. Add remaining salt and pepper.

Place potatoes on serving plates and top with a fillet, skin side up. Spoon lime butter and scatter herbs on top.